# Find the Image of a Point Having the Position Vector: 3hati - 2hatj + Hat K in the Plane Vec R.(3hati - Hat J + 4hatk) = 2 - Mathematics

Find the image of a point having the position vector: 3hati - 2hatj + hat k in the plane vec r.(3hati - hat j + 4hatk) = 2

#### Solution

Let B be the root of point A(3hati - 2hatj + hatk) in the plane vec r(3hati - hatj + 4hatj) = 2can of AB: is

barr(3hati - 2hatj + hatk) + lambda(3hati - hatj + 4hatk)

:. (x - 3)/3 = (y + 2)/(-1) = (z-1)/4 = lambda

:. x = 3lambda + 3,  y = -lambda -2, z = 4lambda + 1

subtitute x,y and z in plane 3x - y + 4z = 2

∴ 3(3lambda + 3)-(-lambda - 2) + 4(4lambda + 1) = 2

9lambda + 9 + lambda + 2 + 16lambda + 4 = 2

26lambda + 13 = 0 => lambda = -1/2

:. x = -3/2 + 3, y = 1/2 - 2 z = -2 + 1

x = 3/2, y = -3/2, z = -1

∴ by midpt formula

3/2 = (3+x_1)/2, (-3)/2 = (-2+y1)/z, -1 = (1-z_1)/2

x_1 = 0  y_1 = -1, -z = 1 - z_1

z_1 = 1+ 2 = 3

Concept: Vector and Cartesian Equation of a Plane
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